Posted by **erika** on Saturday, February 4, 2012 at 11:24am.

a steamboat travels 9 miles up a river in 3 hours and returns the same distance down the river in 2 hours. find the speed of the boat in still water and the rate of the current.

- algebra -
**Reiny**, Saturday, February 4, 2012 at 11:31am
speed of boat in still water --- x mph

speed of current --- y mph

distance up river = time (rate) = 3(x-y) = 9

3x-3y = 9

x-y=3

distance down river = 2(x+y) = 9

2x+2y=9

multiply first by 2

2x-2y = 6

2x+2y = 9

add them

4x = 15

x = 15/4 = 3.75 mph

then in x-y = 3

3.75-y = 3

y = .75 mph

the boat has a speed of 3.75 mph in still water, and

the current has a speed of .75 mph

check:

speed with the current = 4.5

distance = 2(4.5) = 9

speed against current = 3

distance = 3(3) = 9

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